library(dplyr)
library(tidyr)
library(ggplot2)
theme_set(theme_minimal())
Contemplating about the weather, I wondered if I could find out the “most unusual” and “most ideal” years regarding air temperature in Germany, i.e. if I could identify the years in which the daily temperature deviated the most and the least from the expected seasonal temperature. So I decided to look into historical climate data, created an extremely simplified seasonal temperature model and then investigated the deviations from that model.
I retrieved the historical climate data for Germany from 1950 to now from the German Meteorological Service (Deutscher Wetterdienst – DWD). The data come as delimited files with semicolon as column separator. Historical data until 2022 and present data from 2022 to now come as separate files.
raw_hist <- read.delim('data/produkt_klima_tag_19500101_20221231_00403.txt', sep = ';')
head(raw_hist)
## STATIONS_ID MESS_DATUM QN_3 FX FM QN_4 RSK RSKF SDK SHK_TAG NM VPM
## 1 403 19500101 -999 -999 -999 5 2.2 7 -999 0 5.0 4.0
## 2 403 19500102 -999 -999 -999 5 12.6 8 -999 0 8.0 6.1
## 3 403 19500103 -999 -999 -999 5 0.5 1 -999 0 5.0 6.5
## 4 403 19500104 -999 -999 -999 5 0.5 7 -999 0 7.7 5.2
## 5 403 19500105 -999 -999 -999 5 10.3 7 -999 0 8.0 4.0
## 6 403 19500106 -999 -999 -999 5 7.2 8 -999 12 7.3 5.6
## PM TMK UPM TXK TNK TGK eor
## 1 1025.6 -3.2 83 -1.1 -4.9 -6.3 eor
## 2 1005.6 1.0 95 2.2 -3.7 -5.3 eor
## 3 996.6 2.8 86 3.9 1.7 -1.4 eor
## 4 999.5 -0.1 85 2.1 -0.9 -2.3 eor
## 5 1001.1 -2.8 79 -0.9 -3.3 -5.2 eor
## 6 997.5 2.6 79 5.0 -4.0 -4.0 eor
raw_pres <- read.delim('data/produkt_klima_tag_20221107_20240509_00403.txt', sep = ';')
head(raw_pres)
## STATIONS_ID MESS_DATUM QN_3 FX FM QN_4 RSK RSKF SDK SHK_TAG NM VPM
## 1 403 20221107 -999 -999 -999 10 0.0 6 4.5 0 6.2 9.6
## 2 403 20221108 -999 -999 -999 10 0.2 6 7.5 0 6.0 10.4
## 3 403 20221109 -999 -999 -999 10 1.0 6 3.7 0 6.6 11.4
## 4 403 20221110 -999 -999 -999 10 0.0 0 6.1 0 5.1 10.2
## 5 403 20221111 -999 -999 -999 10 0.0 0 1.9 0 6.3 9.6
## 6 403 20221112 -999 -999 -999 10 0.0 0 7.3 0 4.0 8.8
## PM TMK UPM TXK TNK TGK eor
## 1 1002.9 10.7 75 15.0 6.4 5.1 eor
## 2 1002.7 12.1 75 16.9 7.9 4.2 eor
## 3 1001.5 11.8 83 15.0 9.0 5.1 eor
## 4 1012.6 11.7 74 14.3 8.6 5.8 eor
## 5 1020.1 8.6 87 12.8 4.0 0.6 eor
## 6 1022.8 6.4 92 13.8 1.8 -0.9 eor
After reading in the files, we merge them, select only the necessary variables, transform the dates and remove duplicates (since the historical and the present data both contain observations from 2022):
meas <- bind_rows(raw_hist, raw_pres) |>
select(date = MESS_DATUM, temp = TMK) |>
mutate(date = as.POSIXct(strptime(date, "%Y%m%d")),
year = as.integer(as.numeric(format(date, "%Y"))),
day = as.integer(as.numeric(format(date, "%j")))) |> # day of the year as decimal number from 1 to 366
distinct(date, .keep_all = TRUE) # remove duplicates
rm(raw_hist, raw_pres)
stopifnot(all(count(meas, date)$n == 1)) # make sure there are no duplicates
head(meas)
## date temp year day
## 1 1950-01-01 -3.2 1950 1
## 2 1950-01-02 1.0 1950 2
## 3 1950-01-03 2.8 1950 3
## 4 1950-01-04 -0.1 1950 4
## 5 1950-01-05 -2.8 1950 5
## 6 1950-01-06 2.6 1950 6
ggplot(meas, aes(date, temp)) +
geom_line() +
geom_smooth(method = "gam")
filter(meas, year >= 2018) |>
ggplot(aes(date, temp)) +
geom_line()
filter(meas, year == 2023) |>
ggplot(aes(date, temp)) +
geom_line() +
geom_smooth()
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
ggplot(meas, aes(day, temp, color = year)) +
geom_point(alpha = 0.25) +
scale_color_binned(type = 'viridis')
m1 <- lm(temp ~ cos(2 * pi * day/366) + sin(2 * pi * day/366), meas)
summary(m1)
##
## Call:
## lm(formula = temp ~ cos(2 * pi * day/366) + sin(2 * pi * day/366),
## data = meas)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.3493 -2.5635 -0.0229 2.5823 14.0507
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.41121 0.02290 410.93 <2e-16 ***
## cos(2 * pi * day/366) -9.00711 0.03244 -277.66 <2e-16 ***
## sin(2 * pi * day/366) -2.55724 0.03234 -79.08 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.774 on 27155 degrees of freedom
## Multiple R-squared: 0.7544, Adjusted R-squared: 0.7544
## F-statistic: 4.17e+04 on 2 and 27155 DF, p-value: < 2.2e-16
plot(m1)
meas_fit <- cbind(meas, pred = fitted(m1))
filter(meas_fit, year >= 2018) |>
ggplot() +
geom_line(aes(date, temp), alpha = 0.25) +
geom_line(aes(date, pred), color = 'red')
ggplot(meas_fit) +
geom_line(aes(date, temp), alpha = 0.25) +
geom_line(aes(date, pred), color = 'red')
filter(meas_fit, year %in% (1950 + 0:6 * 10)) |>
ggplot(aes(day, temp, color = year)) +
geom_point(alpha = 0.25) +
geom_line(aes(day, pred), color = 'red') +
scale_color_binned(type = 'viridis')
m2 <- lm(temp ~ year + cos(2 * pi * day/366) + sin(2 * pi * day/366), meas)
summary(m2)
##
## Call:
## lm(formula = temp ~ year + cos(2 * pi * day/366) + sin(2 * pi *
## day/366), data = meas)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.0982 -2.5367 -0.0541 2.5753 13.0459
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -47.296595 2.091820 -22.61 <2e-16 ***
## year 0.028544 0.001053 27.11 <2e-16 ***
## cos(2 * pi * day/366) -9.010653 0.032010 -281.50 <2e-16 ***
## sin(2 * pi * day/366) -2.564623 0.031911 -80.37 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.724 on 27154 degrees of freedom
## Multiple R-squared: 0.7609, Adjusted R-squared: 0.7608
## F-statistic: 2.88e+04 on 3 and 27154 DF, p-value: < 2.2e-16
plot(m2)
meas_fit2 <- cbind(meas, pred = fitted(m2))
filter(meas_fit2, year >= 2018) |>
ggplot() +
geom_line(aes(date, temp), alpha = 0.25) +
geom_line(aes(date, pred), color = 'red')
ggplot(meas_fit2) +
geom_line(aes(date, temp), alpha = 0.25) +
geom_line(aes(date, pred), color = 'red')
filter(meas_fit2, year %in% (1950 + 0:6 * 10)) |>
ggplot(aes(day, temp, color = year)) +
geom_point(alpha = 0.25) +
geom_line(aes(day, pred, color = year)) +
scale_color_binned(type = 'viridis')
resid <- meas_fit2$temp - meas_fit2$pred
ggplot(data.frame(resid = resid), aes(resid)) +
geom_histogram(bins = 20)
quantile(abs(resid), 0.9)
## 90%
## 6.015373
thresh_unusal_temp <- 6
resid_stats <- group_by(meas_fit2, year) |>
summarise(me = mean(temp - pred),
mae = mean(abs(temp - pred)),
prop_days_warmer = mean(temp > pred + thresh_unusal_temp),
prop_days_colder = mean(temp < pred - thresh_unusal_temp))
#rmse = sqrt(mean((temp - pred)^2)))
resid_stats
## # A tibble: 75 × 5
## year me mae prop_days_warmer prop_days_colder
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 1950 0.942 2.81 0.0932 0.0329
## 2 1951 1.26 2.83 0.0493 0
## 3 1952 0.00242 2.81 0.0492 0.0246
## 4 1953 1.56 3.04 0.112 0.0137
## 5 1954 -0.258 3.05 0.0493 0.0658
## 6 1955 -0.321 2.96 0.0384 0.0603
## 7 1956 -0.977 3.48 0.0328 0.104
## 8 1957 0.677 3.03 0.0904 0.0301
## 9 1958 0.169 2.48 0.0219 0.0164
## 10 1959 1.04 2.85 0.0822 0.0164
## # ℹ 65 more rows
resid_stats_plt <- pivot_longer(resid_stats, !year, names_to = "measure")
filter(resid_stats_plt, measure %in% c("mae", "me")) |>
ggplot(aes(x = year, y = value, fill = measure)) +
geom_col(position = position_dodge()) +
facet_wrap(vars(measure), nrow = 2, scales = "free_y")
filter(resid_stats_plt, measure %in% c("prop_days_warmer", "prop_days_colder")) |>
ggplot(aes(x = year, y = value, fill = measure)) +
geom_col(position = position_stack()) +
scale_fill_discrete(limits = rev)
resid_stats_ordered <- filter(resid_stats, year < 2024) |>
arrange(mae)
resid_stats_ordered |> head(1)
## # A tibble: 1 × 5
## year me mae prop_days_warmer prop_days_colder
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 2017 -0.188 2.35 0.0274 0.0137
resid_stats_ordered |> tail(1)
## # A tibble: 1 × 5
## year me mae prop_days_warmer prop_days_colder
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 1985 -1.20 3.55 0.0493 0.145
least_deviation_yr <- resid_stats_ordered |> head(1) |> pull(year)
most_deviation_yr <- resid_stats_ordered |> tail(1) |> pull(year)
least_most_plt <- data.frame(year = c(least_deviation_yr, most_deviation_yr), label = c("least deviation", "most deviation")) |>
inner_join(meas_fit2, by = 'year') |>
mutate(label = paste0(year, " (", label, ")"),
resid = temp - pred,
transparency = ifelse(abs(resid) > thresh_unusal_temp, 0.5, 0.1))
ggplot(least_most_plt, aes(day, temp, color = label)) +
geom_point(aes(alpha = transparency)) +
geom_line(aes(day, pred)) +
scale_color_discrete(guide = guide_legend(title = NULL)) +
scale_alpha_identity(guide = NULL)
ggplot(least_most_plt, aes(day, resid, color = label, alpha = transparency)) +
geom_hline(yintercept = 0, linetype = "dashed") +
geom_hline(yintercept = -thresh_unusal_temp, linetype = "dotted") +
geom_hline(yintercept = thresh_unusal_temp, linetype = "dotted") +
geom_point() +
scale_color_discrete(guide = guide_legend(title = NULL)) +
scale_alpha_identity(guide = NULL)
ggplot(least_most_plt, aes(day, temp, color = label)) +
geom_smooth(method = "loess", span = 0.2) +
geom_line(aes(day, pred), linetype = "dashed") +
scale_color_discrete(guide = guide_legend(title = NULL)) +
scale_alpha_identity(guide = NULL)
## `geom_smooth()` using formula = 'y ~ x'